Abstract
Perfectly secure message transmission (PSMT), a problem formulated by Dolev, Dwork, Waarts and Yung, involves a sender \({\cal S}\) and a recipient \({\cal R}\) who are connected by n synchronous channels of which up to t may be corrupted by an active adversary. The goal is to transmit, with perfect security, a message from \({\cal S}\) to \({\cal R}\). PSMT is achievable if and only if n > 2t.
For the case n > 2t, the lower bound on the number of communication rounds between \({\cal S}\) and \({\cal R}\) required for PSMT is 2, and the only known efficient (i.e., polynomial in n) two-round protocol involves a communication complexity of O(n 3ℓ) bits, where ℓ is the length of the message. A recent solution by Agarwal, Cramer and de Haan is provably communication-optimal by achieving an asymptotic communication complexity of O(nℓ) bits; however, it requires the messages to be exponentially large, i.e., ℓ = Ω(2n).
In this paper we present an efficient communication-optimal two-round PSMT protocol for messages of length polynomial in n that is almost optimally resilient in that it requires a number of channels n ≥ (2 + ε)t, for any arbitrarily small constant ε > 0. In this case, optimal communication complexity is O(ℓ) bits.
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Fitzi, M., Franklin, M., Garay, J., Vardhan, S.H. (2007). Towards Optimal and Efficient Perfectly Secure Message Transmission. In: Vadhan, S.P. (eds) Theory of Cryptography. TCC 2007. Lecture Notes in Computer Science, vol 4392. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70936-7_17
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